no. 2
An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle
Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 2, pp. 115-153.
partie suivante An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. - Part II : Petrov type D space-times 
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     title = {An explicit determination of the {Petrov} type {N} space-times on which the conformally invariant scalar wave equation satisfies {Huygens'} principle},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {115--153},
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     number = {2},
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     mrnumber = {839281},
     zbl = {0595.35067},
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     url = {http://www.numdam.org/item/AIHPA_1986__44_2_115_0/}
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Carminati, J.; McLenaghan, R. G. An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Annales de l'I.H.P. Physique théorique, Tome 44 (1986) no. 2, pp. 115-153. http://www.numdam.org/item/AIHPA_1986__44_2_115_0/

[1] L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307-326. | MR | Zbl

[2] R. Bach, Zur Weylschen Relativitats theorie. Math. Zeitscher, t. 9, 1921, p. 110-135. | JFM | MR

[3] Y. Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math., t. 88, 1952, p. 141-225. | MR | Zbl

[4] J. Carminati and R.G. Mclenaghan, Some new results on the validity of Huygens' principle for the scalar wave equation on a curved space-time. Article in Gravitation, Geometry and Relativistic Physics, Proceedings of the Journées Relativistes 1984, Aussois, France, edited by Laboratoire Gravitation et Cosmologie Relativistes. Institut Henri Poincaré, Lecture Notes in Physics, t. 212, Springer-Verlag, Berlin, 1984. | MR | Zbl

[5] J. Carminati and R.G. Mclenaghan, Determination of all Petrov type-N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Phys. Lett., t. 105 A, 1984, p. 351-354. | MR

[6] R. Courant and D. Hilbert, Methods of mathematical physics, t. 2, Interscience, New York, 1962. | Zbl

[7] R. Debever, Le rayonnement gravitationnel, le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. | MR

[8] A. Douglis, The problem of Cauchy for linear hyperbolic equations of second order. Comm. Pure Appl. Math., t. 7, 1954, p. 271-295. | MR | Zbl

[9] J. Ehlers and K. Kundt, Exact solutions of the gravitational Field equations. Article in Gravitation an introduction to current research; edited by L. Witten, Wiley, New York, 1964.

[10] F.G. Friedlander, The wave equation in a curved space-time. Cambridge University Press, Cambridge, 1975. | MR | Zbl

[11] P. Günther, Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus. S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur. K., t. 100, 1952, p. 1-43. | MR | Zbl

[12] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103-106. | MR | Zbl

[13] P. Günther, Einige Sätze uber huygenssche Differentialgleichungen. Wiss. Zeitschr. Karl Marx Univ., Math.-natu. Reihe Leipzig, t. 14, 1965, p. 497-507. | MR | Zbl

[14] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygensshes Prinzip I. Math. Nach., t. 63, 1974, p. 97-121. | MR | Zbl

[15] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923. | JFM

[16] J. Hadamard, The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510-522. | MR | Zbl

[17] E. Hölder, Poissonsche Wellenformel in nicht euclidischen Raumen. Ber. Verh. Sachs. Akad. Wiss. Leipzig, t. 99, 1938, p. 53-66. | JFM | Zbl

[18] H.P. Künzle, Maxwell Fields satisfying Huygens' principle. Proc. Cambridge Philos. Soc., t. 64, 1968, p. 779-785.

[19] J. Leray, Hyperbolic Partial Differential Equations. Mimeographed Notes, Institute of Advanced Study, Princeton.

[20] M. Mathisson, Eine Lösungsmethode fur Differentialgleichungen vom normalen hyperbolischen Typus. Math. Ann., t. 107, 1932, p. 400-419. | JFM

[21] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes. Acta Math., t. 71, 1939, p. 249-282. | MR | Zbl

[22] R.G. Mclenaghan, An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle. Proc. Cambridge Philos. Soc., t. 65, 1969, p. 139-155. | MR | Zbl

[23] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times. Proc. Roy. Soc. London, t. A 327, 1972, p. 229-249. | MR | Zbl

[24] R.G. Mclenaghan, On the validity of Huygen's principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions. Ann. Inst. Henri Poincaré, t. A 20, 1974, p. 153-188. | Numdam | MR | Zbl

[25] R.G. Mclenaghan, Huygens' principle. Ann. Inst. Henri Poincaré, t. A 27, 1982, p. 211-236. | Numdam | MR | Zbl

[26] E.T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys., t. 3, 1962, p. 566-578. | MR | Zbl

[27] B. Rinke and V. Wünsch, Zum Huygenschen Prinzip bei der skalaren Wellengleichung. Beitr. zur Analysis, t. 18, 1981, p. 43-75. | MR | Zbl

[28] R. Penrose, A spinor approach to general relativity. Ann. Physics, t. 10, 1960, p. 171- 201. | MR | Zbl

[29] A.Z. Petrov, Einstein-Raume. Akademie Verlag, Berlin, 1964. | MR | Zbl

[30] F.A.E. Pirani, Introduction to gravitational radiation theory. Article in Lectures on General Relativity, edited by S. Deser and W. Ford, Brandeis Summer Institute in Theoretical Physics, t. 1, 1964, Prentice-Hall, New York.

[31] R. Schimming, Zur Gültigkeit des huygensschen Prinzips bei einer speziellen Metrik. Z. A. M. M., t. 51, 1971, p. 201-208. | MR | Zbl

[32] S.L. Sobolev, Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Mat. Sb. (N. S.), t. 1, 1936, p. 39-70. | JFM | Zbl

[33] K.L. Stellmacher, Ein Beispiel einer Huygensschen Differentialgleichung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., 11, t. 10, 1953, p. 133-138. | MR | Zbl

[34] K.L. Stellmacher, Eine Klasse Huygenscher Differentialgleichungen und ihre Integration. Math. Ann., t. 130, 1955, p. 219-233. | MR | Zbl

[35] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen. Math. Nachr., t. 47, 1970, p. 131-154. | MR | Zbl

[36] V. Wünsch, Maxwellsche Gleichungen und Huygensches Prinzip II. Math. Nach., t. 73, 1976, p. 19-36. | MR | Zbl

[37] V. Wünsch, Uber eine Klasse Konforminvarianter Tensoren. Math. Nach., t. 73, 1976, p. 37-58. | MR | Zbl

[38] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I. Beitr. zur Analysis, t. 12, 1978, p. 47-76. | MR | Zbl

[39] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichunger II. Beitr. zur Analysis, t. 13, 1979, p. 147-177. | MR | Zbl

[40] V. Wünsch, Über ein Problem von McLenaghan. Wiss. Zeit Pädagog. Hochsch. Dr. Theodor Neubaurer. Math.-Natur., t. 20, 1984, p. 123-127. | Zbl